Projector undistortion for high-accuracy fringe projection profilometry

Abstract

Nowadays, fringe projection profilometry is widely used in optical three-dimensional (3D) measurement. However, due to distortion, epipolar constraints are inaccurate for use in correspondence matching of a projector. This results in low accuracy of final 3D reconstruction. To address the issue, two simple and effective methods for undistorted correspondence matching are proposed in this paper. The first removes distortion from projector correspondences using double epipolar constraints; the second pre-distorts the fringe images for projection, thus the projected fringes become naturally undistorted. Comparative experiments are implemented, in a measurement volume of (50 × 30 × 8) mm. The results show that typical mean reconstruction errors of the two methods drop to 32.9% and 27.6% from that of an existing method based on single epipolar-constraint undistortion.

Real-time compensation of projector lens distortion using a linear-grid model in fringe projection profilometry

“…(3) are bivariate continuous functions involving variables x˜up and y˜up. And in practice, the value of distortion error is usually several pixel distances on the entire image and only a dozen or so pixel distances in the extreme case of the image edge farthest from the principal point 17 , 23 . Consequently, neighboring numerical variations on the image tend to display a smooth transition.…”

“…[12][13][14][15][16] Post-undistortion methods refer to the numerical calculation of fringe patterns captured by the camera to correct for distortion. [17][18][19] Xing and Guo 20 used a distorted polynomial model to iteratively solve distorted points to obtain undistorted points, effectively reducing pixel errors. Lv et al 21 constructed a deep neural network and trained it using multiple sets of ceramic plate patterns.…”

“…Post-undistortion methods refer to the numerical calculation of fringe patterns captured by the camera to correct for distortion 17 – 19 Xing and Guo 20 used a distorted polynomial model to iteratively solve distorted points to obtain undistorted points, effectively reducing pixel errors.…”

“…Although the one-direction fringe pattern cannot obtain the specific coordinate of the distorted point, the approximate coordinate of the distorted point can be obtained through linear epipolar constraint. 6,11,17 We employ the linear epipolar equation, as described in Ref. 27, the expression for this equation is E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 1 0 ; 1 1 7 ; 5 2 0…”